Does the order of roots matter in homogeneous linear differential equations?

[kdinser]

When you are trying to determine the general solution of a homogeneous linear ordinary differential equation, after you find the roots, how do you decide which goes with c1 and which goes with c2?

example:

y''-3y'+2y=0

Factoring the auxiliary equation

m^2-3m+2=0=(m-1)(m-2)

is there some kind of convention as to which gets named as m1 and m2?
It seems like every time I do one of these kinds of problems, my answer is the opposite of the books. Is there any difference between

y=c1e^(x)+c2e^(2x) and y=c1e^(2x)+c2e^(x)?

 

[Kelvin]

c1 and c2 are arbitrary constants which must be determined by initial conditions only. so there is no difference if you interchange them

 

[kdinser]

That's what I was hoping for, thanks.

 

[vincentchan]

Is there any difference between

y=c1e^(x)+c2e^(2x) and y=c1e^(2x)+c2e^(x)?

No, they have no different... you can write it either way...

is there some kind of convention as to which gets named as m1 and m2?

It depend on the publisher...

 

[dextercioby]

When you are trying to determine the general solution of a homogeneous linear ordinary differential equation, after you find the roots, how do you decide which goes with c1 and which goes with c2?

example:

y''-3y'+2y=0

Factoring the auxiliary equation

m^2-3m+2=0=(m-1)(m-2)

is there some kind of convention as to which gets named as m1 and m2?
It seems like every time I do one of these kinds of problems, my answer is the opposite of the books. Is there any difference between

y=c1e^(x)+c2e^(2x) and y=c1e^(2x)+c2e^(x)?

Read the result from right to left.I'm sure it will coincide with yours...

Daniel.